Deployable Structure for Use in Establishing a Reflectarray Antenna

ABSTRACT

A deployable structure for use in establishing a reflectarray antenna is provided that includes a flexible reflectarray and a deployment structure that includes an endless pantograph for deploying the flexible reflectarray from a folded, undeployed state towards a deployed state in which the flexible reflectarray is substantially planar. In a particular embodiment, the deployment structure includes a plurality of tapes that engage the endless pantograph and are used to establish a positional relationship between the deployed reflectarray and another component of the reflectarray antenna.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the priority benefit of U.S. Provisional PatentApplication No. 62/233,115, filed on Sep. 25, 2015, which application isincorporated by reference into this application in its entirety.

FIELD OF THE INVENTION

The invention relates to a deployable structure and, more specifically,to a deployable structure for use in establishing a reflectarrayantenna.

BACKGROUND OF THE INVENTION

In applications requiring a high-gain antenna, there are at least threetypes of antennas that are typically employed, namely, a parabolicantenna, phased-array antenna, and a reflectarray antenna. The basicparabolic antenna includes a parabolic shaped reflector and a feedantenna located at the focus of the paraboloid and directed towards thereflector. The phased-array antenna includes multiple antennas with afeed network that provides a common signal to each of the antennas butwith the relative phase of the common signal being fed to each of theantennas established such that the collective radiation pattern producedby the array of antennas is reinforced in one direction and suppressedin other directions, i.e., the beam is highly directional. In manyapplications, the phased-array antenna is preferred to the parabolicantenna because a phased-array antenna can be realized with a lowerheight profile relative to the parabolic antenna. However, thephased-array antenna typically requires a complicated and/or expensivefeed network and amplifier structures. The basic reflectarray antennaincludes a reflectarray that is flat or somewhat curved and a feedantenna directed towards the reflectarray. The reflectarray includes anarray of radiating elements that each receive a signal from the feedantenna and reradiate the signal. Each of the radiating elements has aphase delay such that the collective reradiated signal produced by thearray of radiating elements is in a desired direction. Importantly, theradiating elements are fed by the feed antenna. As such, relative to thephased-arrayed antenna, the reflectarray avoids the need for a feednetwork to provide a signal to each of the radiating elements.

An application that frequently requires a high-gain antenna is aspace-related application in which the antenna is associated with aspacecraft, e.g., a communication or radar imaging satellite. Suchspace-related applications typically impose an additional requirement ofdeployability on the design of a high-gain antenna, i.e., the antennaneeds to be able to transition from a stowed/undeployed state in whichthe antenna is inoperable or marginally operable to unstowed/deployedstate in which the antenna is operable. As such, the high-gain antennain these applications is coupled with a deployment mechanism that isused to transition the antenna from the stowed/undeployed state to theunstowed/deployed state. Characteristic of many space-relatedapplications for such antennas is that the antenna and deploymentmechanism occupy a small volume in the undeployed state relative to thevolume occupied by the antenna and deployment mechanism in the deployedstate.

One approach for realizing a deployable high-gain antenna suitable foruse on a spacecraft is a parabolic antenna structure that includes awire mesh reflector, a feed antenna, and a deployment mechanism. Thedeployment mechanism operates to transition: (a) the wire mesh reflectorfrom a stowed state in which the reflector is folded to an unstowedstate in which the reflector is supported in a paraboloid-like shape bya frame associated with the deployment mechanism and (b) the wire meshreflector and the feed antenna from an inoperable stowed state in whichthe wire mesh reflector and feed antenna are not operably positionedrelative to one another to an unstowed state in which the wire meshreflector and feed antenna are operatively positioned relative to oneanother. Characteristic of such deployable parabolic antenna structuresis a high part count and the need for a relatively large volume toaccommodate the stowed wire mesh reflector, feed antenna, and deploymentmechanism.

A second approach for realizing a deployable high-gain antenna suitablefor use on a spacecraft is a reflectarray antenna structure thatincludes a two-layer reflectarray membrane, a feed antenna, and aninflatable deployment mechanism. The inflatable deployment mechanismoperates to transition: (a) the reflectarray membrane from a stowedstate in which the membrane is folded to an unstowed state in which theinflated deployment mechanism forms a frame that is used in tensioningthe reflectarray membrane into a flat shape, similar to trampoline and(b) the reflectarray membrane and the feed antenna from an inoperablestowed state in which the reflectarray membrane and feed antenna are notoperably positioned with respect to one another to an unstowed state inwhich the reflectarray membrane and the feed antenna are operablypositioned relative to one another. Characteristic of such a deployablereflectarray are difficulties in understanding the deployment kinematicsand reliability challenges, particularly in space-based applications.

SUMMARY OF THE INVENTION

A deployable structure for use in establishing a reflectarray antenna isprovided that is suitable for use in applications in which elements thatare used to form the reflectarray antenna structure need to transitionfrom an undeployed state in which the elements of the deployablestructure conform to a particular volume in which the elements are notsituated so as to function in a reflectarray antenna to a deployed statein which the elements are situated so as to function in a reflectarrayantenna. One such application for such a deployable structure is as partof a space vehicle, (e.g., a communication or radar imaging satellite)in which elements of the structure typically need to conform to acompact or dimensionally constrained volume for at least a portion ofthe launch of the space vehicle and then be deployed from the compact ordimensionally constrained space so as to facilitate the establishment ofa reflectarray antenna structure that typically occupies a considerablygreater volume.

In one embodiment, a deployable structure is provided that includes: (a)a flexible reflectarray or reflectarray membrane that is capable ofbeing placed in a folded state and in an unfolded state in which theflexible reflectarray can function as part of a reflectarray antenna and(b) a deployment mechanism for transitioning the flexible reflectarraybetween the folded and unfolded states. The deployment mechanismincludes an endless pantograph that is adapted for transitioning betweenan undeployed state in which the endless pantograph has a closed shapewith an undeployed perimeter having a first length and a deployed statein which the endless pantograph has a closed shape with a deployedperimeter having a second length that is greater than the first length.The deployment mechanism also includes an energy providing device thatprovides energy that is used to transition the endless pantographbetween from the undeployed state towards the deployed state. Theendless pantograph is operatively connected to the flexiblereflectarray. Initially, when the deployable structure is in theundeployed state, the flexible reflectarray is in a folded state and theendless pantograph is in an undeployed state characterized by having aperimeter with the first length. To transition the deployable structuretransitions from the undeployed state towards the deployed state, theenergy providing device is used in causing the endless pantograph totransition from the undeployed state in which the endless pantograph hasa perimeter with the first length towards the deployed state, therebyincreasing the perimeter length of the endless pantograph. As aconsequence of the transition of the endless pantograph from theundeployed state towards the deployed state, the attached flexiblereflectarray transitions from the folded state towards the unfoldedstate (typically, relatively flat or planar).

In one embodiment of the deployable structure, the endless pantographhas polygonal shape with at least three sides. Comprising the endlesspantograph are linear sub-pantographs (i.e., pantographs that form theendless pantograph and extend in a substantially straight line whentransitioning between the undeployed and deployed states) associatedwith each side of the polygonal shape and vertex structures that eachextend between an end of one of the sub-pantographs and the end of theimmediately adjacent sub-pantograph. In both the undeployed and deployedstates, the sub-pantographs and vertex structures define a plane polygonwith the linear sub-pantographs defining the edges of the polygon andthe vertex structures defining the vertices of the polygon. In theundeployed state, the sub-pantographs define an undeployed perimeterwith a first length. In a deployed state, the sub-pantographs define adeployed perimeter with a second length that is greater than the firstlength.

In another embodiment of the deployable structure, the endlesspantograph comprises two sets of linear sub-pantographs. The first setof linear sub-pantographs includes three or more linear sub-pantographsthat define the edges of a polygon in the undeployed and deployedstates. The second set of linear sub-pantographs comprises the samenumber of linear sub-pantographs as the first set of linearsub-pantographs and also define the edges of a plane polygon in theundeployed and deployed states. The second set of sub-pantographs islocated within the first set of sub-pantographs and oriented such thateach of the linear sub-pantographs of the second set of sub-pantographsis disposed adjacent to a linear sub-pantograph of the first set oflinear sub-pantographs of substantially the same length. As such, eachlinear sub-pantograph of the first set of linear sub-pantographscorresponds to one of the linear sub-pantographs of the second set oflinear sub-pantographs. Each of the linear sub-pantographs of the firstset of linear sub-pantographs is pivotally connected to thecorresponding linear sub-pantograph of the second set of linearsub-pantographs (i.e., the corresponding linear sub-pantographs form astacked linear sub-pantograph in which the constituent linearsub-pantographs lie in different planes). Further, the twosub-pantographs that form a stacked linear sub-pantograph are offset,i.e. the center or mid-leg pivot points are not collinear when thesub-pantographs are in an undeployed state. An offset of 180° providesthe greatest increase in stiffness relative to a polygonal endlesspantograph with sides formed by single sub-pantographs. However, otheroffsets are feasible. The two sets of linear sub-pantographs can becharacterized as a plurality of composite stacked linear sub-pantographswith each composite stacked linear sub-pantograph having two linearsub-pantographs that are pivotally connected, lie in different planes,and are offset relative to one another. The endless pantograph alsoincludes vertex structures that each extend between an end of acomposite stacked linear sub-pantograph and the end of an adjacentcomposite stacked linear sub-pantograph. The endless pantographstructure with two sets of composite stacked linear sub-pantographs hasan undeployed perimeter length that that is only slightly greater thanthe perimeter length of a comparable endless pantograph with sidesformed by a single set of linear sub-pantographs (i.e., an endlesspantograph with a single set of linear sub-pantographs thatsubstantially has the same perimeter length when fully deployed as theendless pantograph structure with two sets of composite stacked linearsub-pantographs when fully deployed).

In yet another embodiment of the deployable structure, the endlesspantograph comprises at least three composite linear sub-pantographswith each of the at least three composite linear sub-pantographs havinga first linear pantograph that is interlaced with, pivotally connectedto, and offset relative to a second linear pantograph (i.e., aninterlaced linear pantograph in which the two pantographs lie in thesame plane). An offset of 180° provides the greatest increase instiffness relative to endless pantograph with sides formed by a singleset of linear sub-pantographs. However, other offsets are feasible. Avertex structure extends between each end of a composite linearsub-pantograph and the end of an adjacent composite linearsub-pantograph. In this embodiment, the composite linear sub-pantographsthat form each side of the endless pantograph can be characterized ascomposite interlaced linear sub-pantographs. The endless pantographstructure with composite linear sub-pantographs that each employ twointerlaced linear sub-pantographs has an undeployed perimeter lengththat is greater than the perimeter length of a comparable endlesspantograph with composite linear sub-pantographs that each employstacked sub-pantographs (i.e., an endless pantograph with stacked linearsub-pantographs that substantially has the same perimeter length as theendless pantograph with interlaced linear sub-pantographs when fullydeployed).

While endless pantographs with polygonal shapes have certain desirableproperties, an endless pantograph that is circular is also feasible andperhaps desirable in certain applications. Further, endless circularpantographs that are stacked or interlaced are also feasible.

Yet another embodiment of the deployable structure employs a limiter tolimit the extent to which the endless pantograph is deployed. In oneembodiment, the limiter includes a plurality of pins with each pinassociated with a first leg of the endless pantograph and adapted toengage a second leg of the endless pantograph to which the first leg ispivotally attached in a manner that prevents relative rotation betweenthe first and second legs once a desired angle between the first andsecond legs is reached during deployment. In a particular embodiment, apin is associated with the two pivot joints located at the ends of eachleg comprising the endless pantograph. The use of these pins, at leastin endless pantographs with polygonal shapes, serves to limit thedeployment of the endless pantograph, distribute the load, and reducebowing in the deployed linear sub-pantographs (particularly whenrelatively long sub-pantographs are employed).

In a particular embodiment of the deployable structure, the energyproviding device includes one or more springs that provide the energyfor transitioning the endless pantograph and the flexible reflectarrayfrom the undeployed state towards the deployed state. In a particularembodiment, the energy providing device comprises a spring associatedwith each pivot connection between the legs that form the endlesspantograph. When the endless pantograph is in the undeployed state, thesprings cumulatively store sufficient potential energy to transition theendless pantograph from the undeployed state to the deployed state. Inthe regard, when the restraint on the endless pantograph that maintainsthe endless pantograph in the deployed state is removed or reduced, thesprings cause the legs that comprise the endless pantograph to rotaterelative to one another and thereby transition the pantograph from theundeployed state towards the deployed state. Once the endless pantographis in the deployed state, the springs store less potential energy thanin the undeployed state but sufficient potential energy to maintain theendless pantograph in the deployed state based on the forces thedeployed pantograph and reflectarray are reasonably expected toencounter in the relevant application. It should also be appreciatedthat by the use of multiple springs and the use of the multiple springsto store more potential energy than is needed to deploy and maintain thedeployment of the endless pantograph and flexible reflectarray thefailure of one or more springs can be accommodated.

In another embodiment of the deployable structure, the deploymentmechanism includes a deployable tape structure for establishing aspatial relationship between the flexible reflectarray and anothercomponent of a reflectarray antenna. For instance, the deployable tapestructure can be used in establishing the position of a feed antenna,subreflector, or reflectarray subreflector relative to the flexiblereflectarray. In a particular embodiment, the deployment structureincludes at least three deployable tapes, each tape extending from afirst end that is operatively engaged to the endless pantograph to asecond end that is operatively connected to an element that facilitatesthe positioning of the deployed reflectarray (supported by deployedendless pantograph) relative to another component of a reflectarrayantenna. In a particular embodiment, the second end of each of the tapesis operatively connected to or adjacent to a feed antenna of thereflectarray antenna. In the deployed state, the three tapes contributeto the positioning of the deployed endless pantograph and the deployedreflectarray relative to the feed antenna in a reflectarray antenna.More specifically, the deployed tapes and the deployed endlesspantograph substantially define a pyramidic or conic structure. In aparticular embodiment, at least two of the tapes are of differentlengths. As such, the deployable structure, when fully deployed,establishes the reflectarray and the feed antenna in a configurationknown as a reflectarray antenna with an offset feed, i.e., the boresightof the feed antenna is not parallel to a line perpendicular to thedeployed reflectarray. Further, the deployed reflectarray, the endlesspantograph, and the deployed tapes substantially define an obliquepyramid or oblique cone. In a specific embodiment, each of the tapestransitions between an undeployed state characterized by a substantiallyportion of the tape being in a roll and a small portion of the tapeextending linearly and a deployed state characterized by a substantialportion of the tape extending linearly. Further, each of the tapes ispreferably a quasi-dual stable tape that exhibits: (a) a first stablestate when the entire tape is wound or rolled, (b) a second stable statewhen the entire tape is straight, and (c) a propensity to transitiontowards the second stable state when a portion of the tape is in thefirst state and another portion of the tape is in the second state. Assuch, when a significant portion of the tape is rolled but a portion ofthe tape is straight or extends linearly, the tape is storing energythat can subsequently be used to transition the tape towards the secondstable state. The use of such tapes facilitate the deployment of thetapes between the undeployed and deployed states.

In a particular embodiment, the deployable structure is configured sothat, when the structure is in the deployed state, the feed antenna islocated between the deployed flexible reflectarray and the body of asatellite. Stated differently, the deployment mechanism and, morespecifically, the tapes are configured so as to move the endlesspantograph and flexible reflectarray away from the feed antenna and thespacecraft.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A-1F respectively illustrate an embodiment of the deployablestructure for use in establishing a reflectarray antenna in anundeployed state, at the onset of deployment, partially deployed,further partially deployed, yet further partially deployed, and fullydeployed;

FIG. 2 illustrates a portion of a first embodiment of an endlesspantograph structure suitable for use in the deployable structure shownin FIG. 1;

FIG. 3 illustrates a portion of second embodiment of an endlesspantograph structure suitable for use in the deployable structure shownin FIG. 1;

FIG. 4 illustrates a portion of a sub-pantograph of the embodiment of aportion of an endless pantograph illustrated in FIG. 2 and pinsassociated with the ends of two of the legs of the sub-pantograph thatlimit the extent to which the sub-pantograph is deployed;

FIGS. 5A and 5B are two perspective exploded views of two crossing legsof the embodiment of a portion of an endless pantograph illustrated inFIG. 2 that illustrate the mid-point pivot connection between the twolegs and the spring associated with the mid-point pivot connection;

FIG. 6 is a top view of the embodiment of an endless pantograph (in anundeployed state) associated with the deployable structure shown in FIG.1 and the limiting pins associated with the endless pantograph;

FIGS. 7A-7D respectively illustrate the embodiment of the endlesspantograph shown in the FIG. 6 in an undeployed state, at the onset ofdeployment, further partially deployed, and fully deployed;

FIG. 8 illustrates an embodiment of a vertex structure that is used toconnect two of the composite stacked linear sub-pantographs of the ofthe endless pantograph shown in FIG. 6;

FIG. 9 illustrates a connector structure for connecting a flexiblereflectarray to the endless pantograph illustrated in FIG. 6;

FIG. 10 illustrates a connector structure for connecting a tape to theendless pantograph illustrated in FIG. 6;

FIG. 11 illustrates a satellite that includes the deployable structureillustrated in FIGS. 1A-1F and with the flexible reflectarray in thedeployed state;

FIG. 12 illustrates the motorized tape cassettes and feed antennaassociated with the base of the deployment structure shown in FIGS.1A-1F;

FIG. 13 is an exploded view of the motorized tape cassettes, feedantenna, and base of the deployment structure shown in FIGS. 1A-1F; and

FIG. 14 illustrates the base of the deployment structure in FIGS. 1A-1Fand the pairs of serpentine flexures that facilitate rotation of theeach of the motorized tape cassettes about an axis that is perpendicularto the base.

DETAILED DESCRIPTION

With reference to FIGS. 1A-1F, an embodiment of a deployable structure20 for use in establishing a reflectarray antenna (hereinafter referredto as “the deployable structure 20”) is described. The deployablestructure 20 conforms to a design specification which requires thedeployable structure 20, in the undeployed state, to fit within a volumethat is 20 cm×20 cm×25 cm. Additional, the deployable structure 20 isrequired to have a mass of no more than 4 kg. Although the deployablestructure 20 conforms to the this design specification, it should beappreciated that adaptation to other form factors and mass requirementsis feasible.

Generally, the deployable structure 20 includes a canister 22, a feedantenna 24, a flexible reflectarray 26, and a deployment mechanism 28.

With reference to FIGS. 1A-1E, the canister 22 serves to store the feedantenna 24, flexible reflectarray 26, and the deployment mechanism 28 inan undeployed state and provides a base for supporting the feed antenna24, flexible reflectarray 26, and the deployment mechanism 28 in thedeployed state. With reference to FIG. 1A, when the deployable structure20 is in the undeployed state, the canister 22 conforms to the designspecification that requires the undeployed structure to fit within avolume that is 20 cm×20 cm×25 cm. Within this specific volume, the feedantenna 24 occupies a first volume within the canister 22, the flexiblereflectarray 26 is folded so as to conform to a second volume within thecanister 22, and the deployment mechanism 28 is in an undeployed statethat conforms to a third volume within the canister. With reference toFIG. 1F, when the deployable structure 20 is in the deployed state, thecanister 22 and the deployment mechanism 28 cooperate to position thedeployed flexible reflectarray 26 relative to the feed antenna 24 so asto conform to a reflectarray antenna structure with an offset feed,i.e., the boresight of the feed antenna 24 is not parallel to a lineperpendicular to the plane of the deployed flexible reflectarray 26.

With continuing reference to FIGS. 1A-1F, the canister 22 generallycomprises a base 32 and four spring-loaded and latchable doors 34A-34Dthat form the sides of the cube and the top of the cube. A releasablelatch structure 36 holds the doors 34A-34D in the undeployed state shownin FIG. 1A. The releasable latch structure 36 can take a number ofdifferent forms. In the illustrated embodiment, the latch 36 employs ameltable pin that disintegrates upon the application of an electricalcurrent, thereby allowing the spring loaded doors 34A-34D to deploy asshown in FIG. 1B. It should be appreciated that other embodiments of acanister that conforms to the design specification and are suitable foruse the feed antenna 24, flexible reflectarray 26, and deploymentmechanism 28 are feasible. Moreover, embodiments of canisters thatconform to other dimensional requirements and that support otherembodiments of a feed antenna, flexible reflectarray, and deploymentmechanism appropriate for these other dimensional requirements or otherapplication are feasible.

With continuing reference to FIGS. 1A-1E, the feed antenna 24 is anantenna that is capable of feeding the flexible reflectarray 26 when thedeployable structure 20 is in the deployed state. In the illustratedembodiment, the feed antenna 24 is a low-profile phased array antenna.In other embodiments, a horn antenna is employed for the feed antenna.

With continuing reference to FIGS. 1A-1E, the flexible reflectarray 26includes: (a) a first flexible membrane that supports an array ofreflectarray elements and (b) a second flexible membrane that serves asa ground plane in the deployed state. A specified distance between thefirst flexible membrane and the second flexible must be maintained forproper operation of the flexible reflectarray 26 when deployed. Thisspacing can be achieved in a number of different ways. For example,connectors that attached the flexible reflectarray 26 to the deploymentmechanism 28 and the tension applied to the flexible reflectarray 26 bythe deployment mechanism 28 can be used to maintain the required spacingbetween the first and second flexible membranes and with only open spacebetween the two membranes. Another alternative is to place acompressible and flexible dielectric structure between the first andsecond flexible membranes to facilitate the desired spacing between themembranes. Yet another option is to employ substantiallynon-compressible post like structures at various locations between themembranes to facilitate the desired spacing between the membranes.Generally, when the flexible reflectarray 26 is in the deployed state,the outer edge 48 of the reflectarray defines a polygon-like shape thathas catenary-shaped edges instead of straight edges. The flexiblecharacteristic of the flexible reflectarray 26 allows the reflectarrayto be folded so as to fit within a specified volume within the canister22 when the reflectarray is in the undeployed state. Other flexiblereflectarrays known to those skilled in the art are feasible.

With continuing reference to FIGS. 1A-1F, the deployment mechanism 28comprises: (a) an endless pantograph 52 for transitioning the flexiblereflectarray 26 between an undeployed, folded state and a deployed statein which the flexible reflectarray 26 is substantially planar and (b) atape dispensing structure 54 that operates to position the feed antenna24 and the flexible reflectarray 26 relative to one another so toconform to a reflectarray antenna structure with an offset feed.Characteristic of the endless pantograph 52 and other endlesspantographs is that the pantograph forms a closed loop and the perimeterdefined by the pantograph has a first length in the undeployed state anda second length that is greater than the first length when thepantograph is transitioning from the undeployed state towards and at thedeployed state.

With reference to FIGS. 1A-1F, 2, and 6, the endless pantograph 52 is anendless polygonal pantograph, i.e., the pantograph has a polygonal shapewhen undeployed and when fully deployed. More specifically, thepantograph 52 is a composite polygonal pantograph that includes twoeight-sided polygonal sub-pantographs. In the illustrated embodiment,each of the eight-sided polygonal sub-pantographs comprises eight linearsub-pantographs with each linear sub-pantograph having one end attachedto the end of a second linear sub-pantograph and the other end attachedto a third linear sub-pantograph. The pantograph 52 is more specificallycharacterized as a stacked polygonal pantograph with: (a) a firsteight-sided polygonal sub-pantograph 76A in which the links of thepantograph occupy a first polygonal cylindrical volume and (b) a secondeight-sided polygonal sub-pantograph 76B in which the links of thepantograph occupy a second polygonal cylindrical volume that is withinthe volume defined by the interior surface of the first polygonalcylindrical volume, (c) each side of the second eight-sided polygonalsub-pantograph 76B pivotally engaged to a corresponding side of thefirst eight-sided polygonal sub-pantograph 76A, and (d) each side of thepantograph 52 connected to two adjacent sides of the pantograph. Thepantograph 52 can also be characterized as eight stacked linearsub-pantographs 78A-78H with each stacked linear sub-pantograph havingone end attached to the end of a second stacked linear sub-pantographand the other end attached to a third stacked linear sub-pantograph.Each of the stacked linear sub-pantographs 78A-78H can be characterizedas having a first and second linear sub-pantographs 80A, 80A that arestacked, pivotally attached to one another, and offset by 180°. Whilethe pantograph 52 has eight sides, it should be appreciated that anendless polygonal pantograph can have three or more sides. The pivotalattachment between the first eight-sided polygonal sub-pantograph 76Aand the second eight-sided polygonal sub-pantograph 76B establishes a180° offset between the first and second eight-sided polygonalsub-pantographs. More specifically, the two linear sub-pantographs thatare embodied in each of the stacked linear sub-pantographs 78A-78H havean offset of 180°. This offset renders the pantograph 52 stiffer in thedeployed state than a pantograph in which each side of the pantograph isrealized with single linear sub-pantograph.

With reference to FIGS. 4, 5A, and 5B, at least one of the linearsub-pantographs 80A, 80B of at least one of the stacked linearsub-pantographs 78A-78H employs a limiting structure that limits theextent to which the endless pantograph 52 deploys. To elaborate, each ofthe linear sub-pantographs 80A, 80B has at least one pair of crossinglegs 150A, 150B. Associated with the crossing leg 150A is a pin 152 thatprojects away from the crossing leg and is positioned so as to engageanother leg of the linear sub-pantograph when the relative rotation ofthe two legs during deployment of the pantograph has resulted inestablishing a predetermined angle between the two legs, therebylimiting the deployment of whichever one of the sub-pantographs 80A, 80Bthe pin 152 is associated, as well as the entire endless pantograph 52.In the illustrated embodiment of the endless pantograph 52, each of thelinear sub-pantographs 80A, 80B includes a first set of parallel legs154 and a second set of parallel legs 156. Associated with each fulllength leg of the first set of parallel legs 154 are two pins that eachengage a different leg of the second set of parallel legs 156 to limitthe deployment of the sub-pantograph with which the pins are associated,the deployment of the sub-pantograph to which the sub-pantograph ispivotally attached, and the deployment of the endless pantograph 52. Dueto the offset be the linear sub-pantographs 80A, 80B, there are partiallegs that are shorter than the full length legs. Depending on theimplementation, there may be one pin or no pins that perform a limitingfunction associated with a partial leg. The use of multiple pins tolimit the deployment of the endless pantograph 52 provides redundancy,i.e., one or more pins can fail and the remaining pin or pins stilllimit the deployment as desired. Further, the use of multiple pinsserves with respect to linear sub-pantographs 80A, 80B serves to“stiffen” the pantographs, i.e., reduce the dead band (droop or sag)that may be present when the linear sub-pantograph is deployed,especially when the deployed pantograph extends over a considerabledistance and/or is subject to certain loads. The use of multiple pinsalso reduces tolerancing requirements. Additionally, the use of multiplepins distributes the load being supported by the sub-pantograph over thelength of the pantograph. It should be appreciated by those skilled inthe art that fewer or more pins or comparable structure can be employedwith a sub-pantograph and/or the locations of the pins altered and thebenefits scaled accordingly.

With continuing reference to FIGS. 5A-5B, to provide energy fortransitioning the endless pantograph 52, a spring structure is utilizedthat stores potential energy when the endless pantograph 52 is in theundeployed state. In deployment, this potential energy is converted tokinetic energy to facilitate the transition of the pantograph from theundeployed state towards the deployed state. With reference to FIGS.5A-5B, an embodiment of a spring structure 90 is described. Generally, aspring structure can be located at any pivot point of a pantographassociated with the endless pantograph 52. Further, a single springstructure can potentially provide the energy needed to transition theendless pantograph 52 between the undeployed and deployed states.However, in the illustrated embodiment of the endless pantograph 52, aspring structure is located at each of multiple pivots points of theendless pantograph 52. The spring structure 90 is associated with apivot structure 92 that is used to establish a center pivot pointbetween the pair of crossing legs or links 150A, 150B of an endlesspantograph. The pivot structure 92 includes a first hole 98A associatedwith cross leg 150A, a second hole 98B associated with crossing leg150B, a nut 100, and screw 102 that extends through each of the holesand engages the nut to establish a pivot connection between the crossinglegs 150A, 150B. In a preferred embodiment, the nut 100, screw 102 andholes 98A, 98B implement a full floating axle structure. The springstructure 90 includes a torsion spring 104, a first housing 106A that isassociated with crossing leg 150A and adapted to engage one leg of thespring, and a second housing 106B that is associated with the crossingleg 150B and adapted to engage the other leg of the spring. The firstand second housings 106A, 106B and the torsion spring 112 are designedso that, when the crossing legs 150A, 150B are moved so as to place thelegs in the undeployed state, potential energy is stored in the torsionspring 104.

With reference to FIG. 1A, when the endless pantograph 52 is in theundeployed state, the endless pantograph 52 is constrained by thecanister 22 (which is also in the undeployed state) such that springstructure located at each of the pivots points associated with theendless pantograph 52 is storing potential energy and the cumulativepotential energy stored by all of the spring structures is sufficient todeploy the endless pantograph 52. During deployment, the constraint onthe endless pantograph 52 is removed and the potential energy stored ineach spring structure 90 associated with the endless pantograph 52 isconverted to kinetic energy that is used to transition the endlesspantograph 52 from the undeployed state towards the deployed state. Withreference to FIGS. 7A-7D, the transition of the endless pantograph 52from the undeployed state to the fully deployed state using the springstructures is illustrated. The spring structure 90 is also designed sothat, even when the pantograph 52 is fully deployed, the springstructures cumulatively store potential energy sufficient tosubstantially maintain the endless pantograph 52 in the deployed statefor the reasonably anticipated loads that the pantograph and flexiblereflectarray 26 are expected to encounter. Further, the spring structure90 is also preferably designed to provide sufficient energy to deployand maintain the endless pantograph 52 and flexible reflectarray 26 inthe deployed state even if a predetermined number of the springstructures fail. While the endless pantograph 52 employs a springstructure 90 at each pivot point, embodiments that employ fewer springstructures are feasible. It should be appreciated that many differenttypes of spring structures known to those skilled in the art can beemployed to provide the energy for deploying an endless pantograph,including spring structures that employ different types of springs thatengage the links of an endless pantograph in a different way.

With reference to FIG. 2, the linear sub-pantographs 80A, 80B of each ofthe stacked linear sub-pantographs 78A-78H are pivotally connected toone another. To elaborate, the outer full-length legs of the firstlinear sub-pantograph 80A and the inner full-length legs of the firstlinear sub-pantograph 80A are each adapted for engagement within thefirst linear sub-pantograph 80A at pivot points 81A-81C. If the firstlinear sub-pantograph 80A has any partial legs, the partial legs areadapted for pivotal engagement within the first linear sub-pantograph80A at two pivot points. Similarly, the outer full-length legs of thesecond linear sub-pantograph 80B and the inner full-length legs of thesecond linear sub-pantograph 80B are each adapted for engagement withinthe second linear sub-pantograph 80B at pivot points 81D-81F. If thesecond linear sub-pantograph 80B has any partial legs, the partial legsare adapted for pivotal engagement within the second linearsub-pantograph 80B at two pivot points. With respect to the pivotconnection between the first and second linear sub-pantographs 80A, 80B,the inner full-length legs of the first sub-pantograph 80A and the innerfull-length legs of the second sub-pantograph 80B are each adapted forengagement at pivot points 81G, 81H. Should any of the inner legs of thefirst sub-pantograph 80A or the inner legs of the of the secondsub-pantograph 80B be a partial leg, the partial leg is adapted forengagement at one pivot point.

With reference to FIG. 3, while the endless pantograph 52 employsstacked linear sub-pantographs 78A-78H, an interlaced linearsub-pantograph 160 can also be employed. The interlaced linearsub-pantograph 160 includes a first linear sub-pantograph 162A and asecond linear sub-pantograph 162B that are interlaced with one another.Characteristic of the interlaced linear sub-pantograph 160 is that oneof the two legs forming a crossing pair of legs in the first linearsub-pantograph 162A underlies two legs associated with the second linearsub-pantograph 162B and the other one of the two legs forming a crossingpair of legs in the first linear sub-pantograph 162A overlies two legsassociated with the second linear sub-pantograph 162B. As such, thefirst and second linear sub-pantograph 162A, 162B lie in a common plane.The interlaced linear sub-pantograph 160 can be adapted to employ alimiting structure and/or spring structure comparable to thosestructures described with respect to the stacked linear sub-pantographs78A-78H. It should also be appreciated that in particular circumstancesa circular endless pantograph can be employed (i.e., an endlesspantograph that is circular in the undeployed and deployed states).Further, a circular pantograph can employ a limiting structure andspring structure comparable to those structures described with respectto the stacked linear sub-pantographs 78A-78H.

With reference to FIGS. 8 and 9, a vertex structure 82 is utilized toconnect the end of one of the stacked linear sub-pantographs 78A-78H tothe end of another of the stacked linear pantographs 78A-78H. The vertexstructure 82, in addition to connecting two stacked linear pantographsto one another, also maintains the angle between the two linear stackedpantographs. In the stacked polygonal pantograph embodiment of thepantograph 52, the interior angle between each pair of adjacent linearstacked pantographs is approximately 135°. The vertex structure 82includes: (a) a housing 84A that engages two center pivot points, onecenter pivot point associated with one of the stacked linearsub-pantographs and the other center pivot point associated with theother stacked linear sub-pantograph, (b) a first bushing 84B thatengages the two end pivot points, one end pivot point associated withone of the stacked linear sub-pantographs and the other end pivot pointassociated with the other stacked linear sub-pantograph, and (c) asecond bushing 84C that engages the two end pivot points, one end pivotpoint associated with one of the stacked linear sub-pantographs and theother end pivot point associated with the other stacked linearsub-pantograph. Each of the housing 84A and first and second bushings84B, 84C includes a first pin 85A that is substantially perpendicular toa first face and a second pin 85B that is substantially perpendicular toa second face. The interior angle between the faces is approximately135° and the angle between the two pins is approximately 45°. Each ofthe pins pivotally engages a hole in a leg associated with one of thepantographs such that the link can rotate about the pin. The 45° anglebetween the pairs of pins associated housing 84A and bushings 84B, 84Ccooperate to maintain an approximately 135° interior angle between thetwo pantographs. The vertex structure 82 also includes a pin 86 that islocated within a hole associated with each of the housing 84A andbushings 84B, 84C. The pin 86 is fixed relative to the housing 84A,i.e., linear relative movement between the pin and the housing 84A isprevented. However, linear relative movement between the pin 86 and theother two bushings 84B, 84C is not prevented. When the endlesspantograph 52 is in an undeployed state, the housing 84A is separatedfrom each of the bushings 84B, 84C by approximately half the length of afull-length leg of a stacked linear sub-pantograph. With reference toFIGS. 7A-7D, as the endless pantograph 52 transitions toward thedeployed state, the distance between the housing 84A and each of thebushings 84B, 84C decreases. Further, each of the vertex structures 82operates to maintain the approximately 135° angle between the twostacked linear sub-pantographs engaged by the vertex structure 82 as theendless pantograph 52 transitions between the undeployed and deployedstates.

With reference to FIG. 9, an embodiment of a connector 120 forestablishing a connection between the flexible reflectarray 26 and theendless pantograph 52 is described. Generally, the connector 120includes a tension spring 122A, a first interface 122B for engaging thetension spring 122A and the flexible reflectarray 26, and a secondinterface 122C for engaging the tension spring 122 and the endlesspantograph 52 or, more specifically, the vertex structure 82 of theendless pantograph 52. The first interface 122B employs a spacerstructure 122D to facilitate a desired spacing between the two membranesof the flexible reflectarray 26. In the illustrated embodiment, multipleconnectors 120 are employed, one for connecting the reflectarray to eachof the vertex structures. The use of a tension spring allows stressesplaced on the flexible reflectarray 26 during deployment and possiblyafter full deployment to be accommodated. Other connectors known tothose skilled in the art that are capable of absorbing potentiallyundesirable stresses placed upon the flexible reflectarray 26 arefeasible. Further, in certain applications, a connector that is capableof absorbing such potential stresses may be unnecessary or undesirable.In such applications, a connector with little, if any, ability to absorbsuch stresses can be employed.

With reference to FIGS. 1D-1F and 12-14, the tape dispensing structure54 includes four motorized tape cassettes 130A-130D that respectivelysupport “carpenter” tapes 132A-132D. Each of the tapes 132A-132D has anend that is operatively connected to or wrapped about a spindle of themotorized tape cassette 130A-130D with which the tape is associated.With reference to FIG. 10, the other end of each of the tapes 132A-132Dis operatively connected to one of the vertex structures 82 of theendless pantograph 52. When the tapes 132A-132D are in the undeployedstate, a substantial portion of each of the tapes is wound around thespindle. When the tapes 132A-132C are in the deployed state, asubstantial portion of each of the tapes linearly extends between themotorized tape cassette and the deployed endless pantograph 52 (e.g.,FIG. 1F). Each of the tapes 132A-132D is a quasi-dual stable tape thatexhibits: (a) a first stable state when the entire tape is wound orrolled, (b) a second stable state when the entire tape is straight, and(c) a propensity to transition towards the second stable state when aportion of the tape is in the first state and another portion of thetape is in the second state. As such, when each of the tapes 132A-132Dis in the undeployed state in which a substantial portion of the tape iswound around a spindle and a portion of the tape is straight, each ofthe tapes is storing potential energy that can be used to facilitate thetransition of the tape from undeployed state to the deployed state inwhich a substantially portion of the tape linearly extends between themotorized tape cassette and the deployed endless pantograph 52. Thetapes 132A-132D have different lengths. As such, when the tapes132A-132D are in the deployed state (e.g., FIG. 1F), the feed antenna 24and the deployed, flexible reflectarray 26 are in an offset feedconfiguration in which the boresight of the feed antenna 24 is notparallel to a line perpendicular to the deployed, flexible reflectarray26. In the illustrated embodiment, the tape 132A is longer than tapes132B-132D, tapes 132B, 132C are of substantially the same length, andtape 132D is shorter than tapes 132A-132C.

With continuing reference to FIGS. 1D-1F and 12-14, the tapes 132A-132Dare employed during deployment to move the endless pantograph 52 awayfrom the feed antenna 24. As such, the angle of each of the tapes132A-132D relative to the endless pantograph 52 changes duringdeployment. With reference to FIG. 10, to accommodate this change in theangle, the end of tape 132A is attached to the endless pantograph 52and, more specifically, to the housing 84A by a hinge joint 170. Theother tapes 132B-132D are also attached to the endless pantograph 52 byhinge joints. The opposite ends of each of the tapes 132A-132D alsoaccommodate this change in angle. With reference to FIGS. 12 and 13,each of the motorized tape cassettes 130A-130D is attached to the base32 of the canister 22 by a mounting structure 172. The mountingstructure 172 includes a pair of mounting standards 174A, 174B that areoperatively attached to the base 32. The mounting standards 174A, 174Bsupport a motorized tape cassette such that the cassette can rotateabout an axis that accommodates the noted change in angle of theassociated tape during deployment. In the illustrated embodiment, themounting standard 174A includes a mounting pin 176A that is establishedin a first hole 178A associated with the motorized tape cassette and themounting standard 174B includes a mounting pin 176B that engages asecond hole 178B associated the motorized tape cassette. The pins 174A,174B and the mounting holes 178A, 178B are collinear and define an axisabout which the motorized tape cassette can rotate during deployment ofthe associated tape.

In certain embodiments and in certain situations, the deployment of thetapes may produce a twist, i.e., a rotation of the endless pantograph 52and flexible reflectarray 26 about an axis that is perpendicular to thebase 32. To accommodate such a twist and prevent undue stress from beingplaced on the tapes, the mounting structure 172 associated with each ofthe motorized tape cassettes 130A-130D includes a rotation structure 180that allows the associated motorized tape cassette to rotate about anaxis that is perpendicular to the base 32. In the illustrated embodimentand with reference to FIGS. 13 and 14, the rotation structure 180comprises a pair of serpentine flexures 182A, 182B to which the mountingstandards 174A, 174B are attached. The pair of serpentine flexures 182A,182B also accommodate some translation movement but are biased tofacilitate rotation of the associated motorized tape cassette about anaxis perpendicular to the base 32.

An embodiment of a tape dispensing structure in which three tapes areemployed, rather than four tapes, is feasible. Further, an embodiment inwhich more than four tapes is employed is also feasible. Also feasiblein certain embodiment are other types of extendable structures, such astelescoping rods, tapes that are folded in a serpentine fashion when inan undeployed state and extend linearly in a deployed state,spring-loaded structures characterized by rods or beams with a springstructure extending between the rods or beams that allows the rods orbeams to be folded when undeployed and to adopt an extended structurewhen deployed, to name a few.

Associated with the deployment mechanism 28 are four pairs of lanyards190A-190D with each pair of lanyards operatively attached to the samevertex structure 82 to which one of the tapes 132A-132D is attached. Thefour pairs of lanyards 190A-190D respectively cooperate with the fourtapes 132A-132D to form four truss-like structures that enhance thestability of the deployed endless pantograph 52 and deployed flexiblereflectarray 26. In the undeployed state, each lanyard is stored inlanyard storage device 192 that, in the illustrated embodiment,comprises a group of tubes disposed in a parallel manner. In theundeployed state, the group of tubes store a lanyard such that thelanyard follows a serpentine path. During deployment, each of thelanyards is extracted from its lanyard storage device 192 as the tapes132A-132D are dispensed by the motorized tape cassettes 130A-130D.

With reference to FIGS. 1A-1F, the transition of the deployablestructure 20 between the undeployed and deployed states is described.With reference to FIG. 1A, the deployable structure 20 is in theundeployed state. Deployment commences with an electrical current beingapplied to the meltable pin associated with the releasable latchstructure 36 to release the latch and allow the spring-loaded doors34A-34D to deploy, as shown in FIG. 1B. At this point, the doors 34A-34Dare no longer constraining the endless pantograph 52 or the tapes132A-132D. The spring structures associated with the endless pantograph52 endeavor to deploy the endless pantograph 52. However, the motorizedtapes cassettes 130A-130D allow the operation of the spring structuresto be controlled or damped. In any event, the endless pantograph 52 andthe flexible reflectarray 26 begin to deploy and the tapes 132A-132Dbegin to dispense so as to move the endless pantograph 52 and theflexible reflectarray 26 away from the feed antenna 24, as shown inFIGS. 1D-1F. The deployment of the endless pantograph 52 and theflexible reflectarray 26 continues until further deployment of theendless pantograph 52 is prevented by the limit structure associatedwith the endless pantograph 52, which is the plurality of pins in theillustrated embodiment. At this point, the flexible reflectarray 26 is asubstantially flat or planar and constitutes an operable reflectarray.The deployment of the tapes 132A-132D continues until each of the tapes132A-132D has reached a predetermined length. If the flexiblereflectarray 26 is fully deployed at this point, the tapes 132A-132Dhave positioned the flexible reflectarray 26 relative to the feedantenna 24 so as to operatively position the reflectarray and the feedantenna for use in an reflectarray antenna with an offset feed, as shownin FIG. 1F.

With reference to FIG. 11, a satellite 140 that includes the deployablestructure 20 and other satellite elements 142. The deployable structure20 operates such that upon full deployment, the feed antenna 24 ispositioned between the deployed, flexible reflectarray 26 and the othersatellite elements 142.

In certain embodiments, the potential energy stored in undeployed tapesmay provide sufficient radial force to deploy the endless pantograph andthereby eliminate the need for any spring structure/structuresassociated with the endless pantograph. The operation of such tapes mayor may not be supplemented by the use of one or more electric motors. Ifsupplemented by one or more electric motors, one function of themotor(s) would be to control or dampen the deployment of the tapes. Inyet other embodiments, extendable structures other than tapes can beemployed. For instance, telescoping rods and other extendable structurecan be employed. Further, other extendable structures that employ othermotive forces, such as pneumatic or hydraulic forces, can be employed.It should also be appreciated that the endless pantograph structure isnot limited to deploying a flexible reflectarray. The endless pantographcan be used to deploy other flexible structures in space-basedapplications, such flexible solar panels, solar sails, and the like. Itshould also be appreciated that the endless pantograph can be used todeploy flexible membrane structure other than a flexible reflectarray.For instance, the endless pantograph structure can be used to deploy aflexible solar cell array or solar sail. Further, while the deploymentstructure has largely been described with respect to its use inimplementing an offset reflectarray antenna, the deployment structure isbelieved to be adaptable to the implementation of other reflectarrayantenna structures, such as center fed reflectarray antennas, center fedCassegrain reflectarray antennas, and offset fed Cassegrain reflectarrayantennas, to name a few.

The foregoing description of the invention is intended to explain thebest mode known of practicing the invention and to enable others skilledin the art to utilize the invention in various embodiments and with thevarious modifications required by their particular applications or usesof the invention.

What is claimed is:
 1. A deployable structure for use in establishing a reflectarray antenna structure comprising: a feed antenna for use in a reflectarray antenna structure; a flexible electrical element for use in a reflectarray antenna; wherein the flexible electrical element is folded in an undeployed state; wherein the flexible electrical element is unfolded in a deployed state relative to the undeployed state; and a deployment mechanism for transitioning the flexible electrical element from the undeployed state towards the deployed state; and wherein the deployment mechanism includes an endless pantograph structure and an energy providing device for use in transitioning the endless pantograph structure from the undeployed state towards the deployed state; wherein the endless pantograph forms a closed loop; wherein the endless pantograph structure defines a perimeter that has a first length in the undeployed state and a second length that is greater than the first length when the endless pantograph structure transitions from the undeployed state towards the deployed state; wherein the endless pantograph is operatively engaged to the flexible electrical element; wherein, when the endless pantograph element transitions from the undeployed state towards the deployed state, the flexible electrical element transitions from being folded in the undeployed state towards being unfolded.
 2. A deployable structure for use in establishing a reflectarray antenna, as claimed in claim 1, wherein the endless pantograph includes a first pantograph and a second pantograph that is pivotally connected to the first pantograph.
 3. A deployable structure for use in establishing a reflectarray antenna, as claimed in claim 2, wherein the first and second pantographs are stacked.
 4. A deployable structure for use in establishing a reflectarray antenna, as claimed in claim 2, wherein the first and second pantographs are interlaced.
 5. A deployable structure for use in establishing a reflectarray antenna, as claimed in claim 2, wherein there is a non-zero offset between the first pantograph and second pantograph.
 6. A deployable structure for use in establishing a reflectarray antenna, as claimed in claim 5, wherein the non-zero offset is about 180°.
 7. A deployable structure for use in establishing a reflectarray antenna, as claimed in claim 1, wherein the endless pantograph has a polygon shape with at least first, second, and third sides.
 8. A deployable structure for use in establishing a reflectarray antenna, as claimed in claim 1, further comprising: a limiter for limiting the extent to which the endless pantograph can be deployed.
 9. A deployable structure for use in establishing a reflectarray antenna, as claimed in claim 1, further comprising: a plurality of limiters, each limiter operatively connected to a first leg of the endless pantograph and adapted to engage a second leg of the endless pantograph that is pivotally connected to the first leg when relative rotation of the first and second legs establishes a predetermined angle between the first and second legs and prevent further rotation of the first and second legs relative to one another.
 10. A deployable structure for use in establishing a reflectarray antenna, as claimed in claim 1, wherein the energy providing device includes a spring that operatively engages first and second legs of the endless pantograph, the spring storing a first amount of potential energy in the undeployed state and a second amount of potential energy that is less than the first amount of potential energy when the endless pantograph transitions from the undeployed state towards the deployed state.
 11. A deployable structure for use in establishing a reflectarray antenna, as claimed in claim 1, wherein the energy providing device includes a plurality of springs, wherein each spring of the plurality of springs operatively engages a different pair of legs of the endless pantograph.
 12. A deployable structure for use in establishing a reflectarray antenna, as claimed in claim 1, wherein the energy providing device includes a plurality of springs and each leg of the endless pantograph is engaged by at least two springs of the plurality of springs.
 13. A deployable structure for use in establishing a reflectarray antenna, as claimed in claim 1, wherein the energy providing device includes an electric motor.
 14. A deployable structure for use in establishing a reflectarray antenna, as claimed in claim 1, wherein the energy providing device includes an extendable member.
 15. A deployable structure for use in establishing a reflectarray antenna, as claimed in claim 1, wherein: the deployment mechanism includes a plurality of tapes each having an end that is operatively connected to the endless pantograph and used to support the flexible electrical element at a predetermined position relative to the feed antenna so that the flexible electrical element and the feed antenna can be used in a reflectarray antenna.
 16. A deployable structure for use in establishing a reflectarray antenna comprising: a flexible electrical element for use in a reflectarray antenna; wherein the flexible electrical element is folded in an undeployed state; wherein the flexible electrical element is unfolded in a deployed state relative to the undeployed state; a feed antenna for providing a signal to or receiving a signal from the flexible electrical element in the deployed state; and a deployment mechanism for transitioning the flexible electrical element and the feed antenna from the undeployed state in which the flexible electrical element and the feed antenna are not positioned relative to one another for use in a reflectarray antenna towards a deployed state in which the flexible electrical element and the feed antenna are positioned relative to one another for use in a reflectarray antenna; wherein the deployment mechanism includes an endless pantograph structure for transitioning the flexible electrical element from the undeployed state towards the deployed state; wherein the endless pantograph forms a closed loop; wherein the endless pantograph structure defines a perimeter that has a first length in the undeployed state and a second length that is greater than the first length when the endless pantograph structure transitions from the undeployed state towards the deployed state; wherein the endless pantograph is operatively engaged to the flexible electrical element; wherein, when the endless pantograph structure transitions from the undeployed state toward the deployed state, the flexible electrical structure transitions from being folded in the undeployed state towards being unfolded; wherein the deployment mechanism includes an extendable structure that is operatively connected to the endless pantograph and adapted to support the endless pantograph and flexible electrical element at a deployed position at which the flexible electrical element is positioned to cooperate with the feed antenna for use in a reflectarray antenna.
 17. A deployable structure for use in establishing a reflectarray antenna, as claimed in claim 16, wherein the endless pantograph has a polygon shape with at least three sides.
 18. A deployable structure for use in establishing a reflectarray antenna, as claimed in claim 17, wherein each of the at least three sides of the endless pantograph includes two sub-pantographs that are pivotally connected to one another in one of a stacked manner and interlaced manner.
 19. A deployable structure for use in establishing a reflectarray antenna, as claimed in claim 17, wherein each of the sub-pantographs includes a plurality of pin limiters with each pin limiter adapted to prevent rotation of a first leg of the sub-pantograph relative a second leg of the sub-pantograph when a predetermined relative rotation of the first and second legs to one another establishes a predetermined angle between the first and second legs.
 20. A deployable structure for use in establishing a reflectarray antenna, as claimed in claim 16, wherein the extendable structure includes a tape with a substantial portion of the tape disposed in a non-linear manner in the undeployed state and substantially portion of the tape disposed in a linear manner in the deployed state.
 21. A deployable structure for use in establishing a reflectarray antenna, as claimed in claim 16, wherein the extendable structure includes a plurality of tapes with a substantial portion of each of the tapes disposed in a non-linear manner in the undeployed state and substantially portion of the tape disposed in a linear manner in the deployed state.
 22. A deployable structure for use in establishing a reflectarray antenna, as claimed in claim 16, wherein: a first tape of the plurality of tapes has a first length disposed in a linear manner in the deployed state; a second tape of the plurality of tapes has a second length disposed in a linear manner in the deployed state; wherein the first length of the first tape is different than the second length of the second tape.
 23. A deployable structure for use in establishing a reflectarray antenna, as claimed in claim 22, wherein: a third tape of the plurality of tapes has a third length disposed in a linear manner in the deployed state; wherein the third length is different than the first and second lengths of the first and second tapes.
 24. A deployable structure for use in establishing a reflectarray antenna, as claimed in claim 16, wherein extendable structure is adapted to move the endless pantograph and flexible electrical element from a first location at a first distance from the feed antenna to a second location that is second distance from the feed antenna that is greater than the first distance.
 25. A deployable structure for use in establishing a reflectarray antenna, as claimed in claim 16, wherein: the extendable structure includes a tape cassette for storing a substantial portion of a tape in a roll disposed about a tape axis when the tape is in an undeployed state, a base, and swivel structure that operatively connects the tape cassette to the base; wherein the swivel structure allows the tape cassette to rotate about tape axis and is biased to allow the tape cassette to rotate about an transverse axis that is substantially perpendicular to the tape axis.
 26. A deployable structure for use in establishing a reflectarray antenna, as claimed in claim 25, wherein the swivel structure includes a pair of serpentine flexures.
 27. A deployable structure comprising: a flexible element; wherein the flexible element is folded in an undeployed state; wherein the flexible element is unfolded in a deployed state relative to the undeployed state; and a deployment mechanism for transitioning the flexible element from the undeployed state towards a deployed state; wherein the deployment mechanism includes an endless pantograph structure and an energy providing device for transitioning the endless pantograph structure from the undeployed state towards the deployed state; wherein the endless pantograph forms a closed loop and is adapted to operatively engage the flexible element; wherein the endless pantograph structure defines a perimeter that has a first length in the undeployed state and a second length that is greater than the first length when the endless pantograph structure transitions from the undeployed state towards the deployed state; wherein the endless pantograph is operatively engaged to the flexible element; wherein, when the endless pantograph structure transitions from the undeployed state toward the deployed state, the flexible structure transitions from being folded in the undeployed state towards being unfolded.
 28. A deployable structure for use in establishing a reflectarray antenna, as claimed in claim 27, wherein the endless pantograph includes a first pantograph and a second pantograph that is pivotally connected to the first pantograph and there is an offset between the first and second pantographs of about 180°.
 29. A deployable structure for use in establishing a reflectarray antenna, as claimed in claim 27, wherein the endless pantograph has a polygon shape with at least three sides. 